Hello, I'd like to know if its possible that I can make new extension of stay after transferring info from old passport to new passport without obtaining new non ed visa in my new passport.

Changing your passport doesn't change your immigration status. If you have an extension of stay now, take both passports to immigrations to transfer the extension stamp and any other relevant information from the old passport to the new passport.

They don't transfer visas, but if the visa you had is what you used to enter the country, they'll put the details in your new passport. And, if you would be eligible for a new extension with the old passport, you will still be eligible with the new passport when your current extension expires.

Use this form when you go to immigrations and take photocopies of relevant pages from both passports. http://www.thaivisa.com/forum/files/file/20-transfer-stamp-to-a-new-passport-form/

Most offices would want a letter from your embassy stating that they have issued you the new passport.

There should be no fee from immigrations.